The Nuts and Bolts of Proofs

The Nuts and Bolts of Proof instructs students on the basic logic of mathematical proofs, showing how and why proofs of mathematical statements work. It provides them with techniques they can use to gain an inside view of the subject, reach other results, remember results more easily, or rederive them if the results are forgotten.A flow chart graphically demonstrates the basic steps in the construction of any proof and numerous examples illustrate the method and detail necessary to prove various kinds of theorems.

* The "List of Symbols" has been extended.
* Set Theory section has been strengthened with more examples and exercises.
* Addition of "A Collection of Proofs"

Introduction and Basic Terminology
General Suggestions
Some basic Techniques Used in Proving a Theorem of the Form :If A then B"
Direct Proof
Related Statements
Proof by Contra positive
How to Construct the Negation of a Statement
Special Kinds of Theorems
"If and only if" or Equivalence Theorems
Use of Counterexamples
Mathematical Induction
Existence Theorems
Uniqueness Theorems
Equality of Sets
Equality of Numbers
Composite Statements
Limits
Review Exercises
Exercises without Soultions
Collection of Proofs
Solutions of the Exercises at the End of the Sections and the Review Exercises
Other Books on the Subject of Proofs and Mathematical Writing